Hartmann vs. reverse Hartmann test: a Fourier optics point of view

TL;DR

This paper compares the classical Hartmann and reverse Hartmann wavefront tests using Fourier optics, revealing that the reverse configuration can achieve similar measurement accuracy as the traditional Shack-Hartmann sensor.

Contribution

It provides a Fourier optics-based analysis of both tests and demonstrates the potential of the reverse Hartmann test to match Shack-Hartmann performance.

Findings

Reverse Hartmann test can achieve similar accuracy to Shack-Hartmann.

Fourier optics formalism effectively models both tests.

Numerical simulations support the equivalence in performance.

Abstract

The Shack-Hartmann Wavefront Sensor (WFS) is well-known in the fields of optical metrology, wavefront sensing in astronomy, and ophthalmologic control applications. The purpose of this communication is to bring new insights on the historical Hartmann test and to compare it with the less known reverse Hartmann test, where the locations of the pupil mask and observed image planes are exchanged. Both tests can actually be interpreted by using the formalism of Fourier optics, i.e. Fraunhofer diffraction for the Shack-Hartmann and Fresnel diffraction in the reverse configuration. The principles of these models are firstly described in the communication. The results of numerical simulations are then presented, allowing comparing both optical arrangements from the Fourier optics point of view, in terms of achievable wavefront measurement accuracy. They show that a WFS based on the reverse Hartmann test may globally achieve the same performance as the classical Shack-Hartmann